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Two circles of diameters r and 2r are cut from a circle. The sum of diameters of small circles is equal to the diameter of big circle. The area of uncut portion is 100 π cm2. What is the diameter of the biggest circle out of the three circles?

Two circles of diameters r and 2r are cut from a circle. The sum of diameters of small circles is equal to the diameter of big circle. The area of uncut portion is 100 π cm2. What is the diameter of the biggest circle out of the three circles? Correct Answer 30 cm

Formula used:

Area of a circle with diameter 'd' = (π/4)d2 

Diameter = 2 × radius

Calculation:

Here r and 2r are diameters of circles,

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Diameter of bigger circle = r + 2r = 3r

Area of the bigger circle before cut = π(3r)2/4

⇒ 9πr2/4

Area of cut portion = π(r)2/4 + π(2r)2/4

⇒ 5πr2/4

Area of uncut portion = 9πr2/4 - 5πr2/4

⇒ πr2

∴ πr2 = 100 π

⇒ r = 10 cm

Diameter of bigger circle = 3r

⇒ 3 × 10 = 30 cm

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In question itself given that the diameters are r and 2r, don't confuse with usual notations in the calculation. 

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